Judith Kerr is blaming the rhymes. It's their fault, she says, that her latest picture book is somewhat surreal, featuring flying elephants, lions plucking rabbits from hats and a crocodile and a kangaroo setting off on a bicycle.

Author of the much-loved children's picture books The Tiger Who Came to Tea and the Mog series, about a cat with a mind of its own, Kerr has taken a "quite different" approach for One Night in the Zoo. Speaking on the phone from her long-time home in Barnes, west London – she's lived there for more than 40 years – she says it's unlike anything she's done before.

"Whereas all the other books started with a story, this one started with an idea of pictures. I always say this and it sounds so pretentious – I love Chagall: there's absolutely nothing of him left in the book but that's where I started to think about it," she says. "And I wanted to do animals doing surreal things, really wild stuff ... I could see these images. It's never quite like what I've had in my head but the idea of doing these wild moonlit pictures – once I'd thought of it I had to do it."

So she began with an elephant "who jumped in the air and flew". Coming up with a charmingly cheery elephant taking off against a purpling sky, she knew she was heading in the right direction when she risked showing the picture to her then seven-year-old grandson. "He looked at it and laughed and said 'elephants don't fly ... I think this is going to be a good one'. That was hugely encouraging, because it's quite hard to do, to have the picture in your head of some absurd narrative – you never quite get it as you want it. I was very pleased."

Confident she was on the right path, the rhymes began to take hold. The crocodile – as gentle-looking as Kerr's better-known tiger, the one who came for tea – departs with the kangaroo on a bicycle made for two, "three lions did tricks which astonished a gnu [and] four bears cooked a squid and squidgeberry stew".

"It rhymes, which makes it even more surreal, in a way. The rhyme leads to something you wouldn't otherwise get to," Kerr chuckles. "It was quite hard to find all these rhymes with 'oo'." She recites some of the book to me. "I've loved doing it," she says. "It's rather nice at my great age [she's 86] to do something different, something new."

Despite Kerr's huge success (the Mog picture books and The Tiger Who Came to Tea have collectively sold more than 9m copies), this brand of gentle self-deprecation twists and twines its way through much of our conversation. Talking me through how she works – in a room at the top of her house, surrounded by books, she'll start around 10.30am and keep going as long as there's light – provided she's happy with what she's producing. "Sometimes I'm just producing rubbish so I have to stop. If it's not going well, I think 'why did I ever think I had talent?'"

She worried terribly about the retrospective exhibition celebrating her life and work that launched late last year in Newcastle, at Seven Stories. "I was in a total tizz about it," she says. "They had all my stuff, and I thought, suppose they choose all the really dreadful ones – there are always some – and then suppose they enlarge them … Then I saw it and it was wonderful: so imaginative, beautifully done and very moving. There's a lot about my life – they've even got a photo of my father which I'd never seen."

She is clearly moved by this. Her father, the German drama critic and writer Alfred Kerr, had a price on his head throughout the second world war for speaking out against the Nazi regime (his books were burned by the Nazis). Kerr was just nine years old when the family left Berlin in 1933, the day before the authorities came to arrest them; they passed through Switzerland and France before settling in England in 1936. Kerr wrote about the experience in her vivid, child's-eye memoir, When Hitler Stole Pink Rabbit.

"I remember saying to my father a very long time ago, 'I want to draw – that's what I want to do'. He said, you have to be very very good, because they're very very good in this country," she remembers. Initially, therefore, she took a job in television, which she left to have children. Her first book, The Tiger Who Came to Tea, started life as a story she would tell her two-year-old daughter at bedtime. "She wanted it again and again – although I tried others, that was the one she liked. I kept telling it and telling it until it was totally solid in my head," she says. "But I didn't think of doing anything until almost five years later when the children [she also has a son, the novelist Matthew Kneale] were at school. Then I had the day free from nine to three, and I could do something about it."

She showed The Tiger Who Came to Tea to the publisher Collins who, to her amazement, agreed to publish it. The Mog series, too, was drawn from her home life – an amalgamation of the silly antics of the family's cats. "[The original] Mog didn't miaow; she thought the children were making so much noise it wasn't necessary. Instead, she'd make terrible faces outside when she couldn't use the cat flap. So the first Mog book was all about the things she did," she says. "I hadn't meant to do any more Mog books, but we kept getting more cats – the children wanted kittens. And they all started doing odd things. One was afraid of heights and got stuck on the roof, another was frightened of the Christmas tree ... They're very funny creatures. My present one goes for walks with me."

More than 40 years after her enigmatically smiling tiger first captured the imaginations of the nation's children, Kerr insists that she's "still very surprised it worked out like this". "My practical brother and mother were very worried about me – I never had any money and always looked awful," she remembers. "I think an awful lot of it is down to my husband [the late Nigel Kneale, scriptwriter and creator of Quatermass]. I was painting and got the odd prize, but it was a bit of a slog. Once I met him, everything fell into place. He encouraged me always, made me feel I was alright. I don't know if I would ever have done anything much if it hadn't been for him. He was a terrific help, a great delight."

Kneale, known by the family as Tom, died in 2006, and his loss is obviously still raw. As a result, Kerr has thrown herself into work, and hates not having something lined up to do. "When I did the last little bit of One Night in the Zoo I panicked," she says. "I thought 'now what? What am I going to do next?' I don't think I minded when Tom was alive; it was nice not to be working for a little while, particularly if he wasn't – we'd go out and do things together. But now I'm on my own I hate not working."

So she's already two-thirds of the way through a new book – due out in 2011 – about an old lady. "It's ridiculous, too, but a little more about something – for children, but maybe of interest to old ladies, too, I suppose," she says, before ending with a typically Kerr-ian piece of diffidence: "I hope I live long enough to see it published."